Fundamental Frequency Estimation

As mentioned in §4.10.2 above, it is advisable to estimate the fundamental frequency of vibration (often called ``F0'') in order that the partial overtones are well resolved while maintaining maximum time resolution for estimating the decay time-constant.

Below is a summary of the F0 estimation method used in calibrating loop filters with good results [447]:

• Take an FFT of the middle third of a recorded plucked string tone.
• Find the frequencies and amplitudes of the largest $K$ peaks, where $K$ is chosen so that the $K$ retained peaks all have a reasonable signal-to-noise ratio.
• Form a histogram of peak spacing $\Delta f_i$
• The pitch estimate ${\hat f}_0$ is defined as the most common spacing $\Delta f_i$ in the histogram.

The F0 estimate so formed is sufficiently accurate for purposes of calibrating a peak tracker for decay-rate estimation. (The F0 value is only used to set the FFT window length in the STFT to four or nominal periods under the window, so it is not critical.)